Answer:
See below for proof.
Step-by-step explanation:
We are given that ABCD is an isosceles trapezoid, and that segment AB is congruent to segment DC.
Since the base angles of a trapezoid are congruent, then ∠ABC ≅ ∠DCB.
The reflexive property of congruence states that any geometric figure is congruent to itself, so we can say that BC ≅ BC.
Now, we can state that triangles ABC and BCD are congruent by Side-Angle-Side (SAS) congruency, since two sides and the included angle of triangle ABC are congruent to the corresponding sides and angle of triangle BCD.
Since we have proved that triangles ABC and BCD are congruent, then their corresponding angles, sides, and vertices are also congruent by CPCTC (Corresponding Parts of Congruent Triangles are Congruent).
[tex]\begin{array}{l|l}\sf Statement&\sf Reason\\\cline{1-2}\vphantom{\dfrac12}\textsf{$ABCD$ is an isosceles trapezoid}&\sf Given\\\vphantom{\dfrac12}\overline{AB}\cong\overline{DC}&\sf Given\\\vphantom{\dfrac12}\angle ABC\cong\angle DCB&\textsf{Base angles of a trapezoid are congruent}\\\vphantom{\dfrac12}\overline{BC}\cong\overline{BC}&\textsf{Reflexive property of congruence}\\\vphantom{\dfrac12}\triangle ABC\cong\triangle BCD&\textsf{SAS congruency}\\\vphantom{\dfrac12}AC\cong BD&\sf CPCTC}\end{array}[/tex]
